Properties

Label 882.4.g.bd.361.2
Level $882$
Weight $4$
Character 882.361
Analytic conductor $52.040$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 882.g (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(52.0396846251\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} + 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 7^{2} \)
Twist minimal: no (minimal twist has level 294)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.2
Root \(0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 882.361
Dual form 882.4.g.bd.667.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(7.94975 + 13.7694i) q^{5} +8.00000 q^{8} +O(q^{10})\) \(q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(7.94975 + 13.7694i) q^{5} +8.00000 q^{8} +(15.8995 - 27.5387i) q^{10} +(28.6985 - 49.7072i) q^{11} -5.69848 q^{13} +(-8.00000 - 13.8564i) q^{16} +(25.9497 - 44.9463i) q^{17} +(8.10051 + 14.0305i) q^{19} -63.5980 q^{20} -114.794 q^{22} +(-106.698 - 184.807i) q^{23} +(-63.8970 + 110.673i) q^{25} +(5.69848 + 9.87007i) q^{26} +218.191 q^{29} +(-125.698 + 217.716i) q^{31} +(-16.0000 + 27.7128i) q^{32} -103.799 q^{34} +(-193.397 - 334.973i) q^{37} +(16.2010 - 28.0610i) q^{38} +(63.5980 + 110.155i) q^{40} -328.503 q^{41} -37.5879 q^{43} +(114.794 + 198.829i) q^{44} +(-213.397 + 369.614i) q^{46} +(127.497 + 220.832i) q^{47} +255.588 q^{50} +(11.3970 - 19.7401i) q^{52} +(105.794 - 183.240i) q^{53} +912.583 q^{55} +(-218.191 - 377.918i) q^{58} +(206.101 - 356.977i) q^{59} +(-418.347 - 724.598i) q^{61} +502.794 q^{62} +64.0000 q^{64} +(-45.3015 - 78.4645i) q^{65} +(82.7939 - 143.403i) q^{67} +(103.799 + 179.785i) q^{68} +465.015 q^{71} +(224.829 - 389.415i) q^{73} +(-386.794 + 669.947i) q^{74} -64.8040 q^{76} +(171.779 + 297.530i) q^{79} +(127.196 - 220.310i) q^{80} +(328.503 + 568.983i) q^{82} +1502.33 q^{83} +825.176 q^{85} +(37.5879 + 65.1041i) q^{86} +(229.588 - 397.658i) q^{88} +(170.543 + 295.389i) q^{89} +853.588 q^{92} +(254.995 - 441.664i) q^{94} +(-128.794 + 223.078i) q^{95} +865.437 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 4q^{2} - 8q^{4} + 12q^{5} + 32q^{8} + O(q^{10}) \) \( 4q - 4q^{2} - 8q^{4} + 12q^{5} + 32q^{8} + 24q^{10} - 4q^{11} + 96q^{13} - 32q^{16} + 84q^{17} + 72q^{19} - 96q^{20} + 16q^{22} - 308q^{23} - 18q^{25} - 96q^{26} + 160q^{29} - 384q^{31} - 64q^{32} - 336q^{34} - 536q^{37} + 144q^{38} + 96q^{40} - 1512q^{41} + 800q^{43} - 16q^{44} - 616q^{46} + 312q^{47} + 72q^{50} - 192q^{52} - 52q^{53} + 2304q^{55} - 160q^{58} + 864q^{59} - 1416q^{61} + 1536q^{62} + 256q^{64} - 300q^{65} - 144q^{67} + 336q^{68} + 3048q^{71} - 744q^{73} - 1072q^{74} - 576q^{76} - 976q^{79} + 192q^{80} + 1512q^{82} + 624q^{83} + 1400q^{85} - 800q^{86} - 32q^{88} + 108q^{89} + 2464q^{92} + 624q^{94} - 40q^{95} - 1488q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 1.73205i −0.353553 0.612372i
\(3\) 0 0
\(4\) −2.00000 + 3.46410i −0.250000 + 0.433013i
\(5\) 7.94975 + 13.7694i 0.711047 + 1.23157i 0.964464 + 0.264213i \(0.0851120\pi\)
−0.253417 + 0.967357i \(0.581555\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 8.00000 0.353553
\(9\) 0 0
\(10\) 15.8995 27.5387i 0.502786 0.870851i
\(11\) 28.6985 49.7072i 0.786629 1.36248i −0.141392 0.989954i \(-0.545158\pi\)
0.928021 0.372528i \(-0.121509\pi\)
\(12\) 0 0
\(13\) −5.69848 −0.121575 −0.0607875 0.998151i \(-0.519361\pi\)
−0.0607875 + 0.998151i \(0.519361\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −8.00000 13.8564i −0.125000 0.216506i
\(17\) 25.9497 44.9463i 0.370220 0.641240i −0.619379 0.785092i \(-0.712616\pi\)
0.989599 + 0.143852i \(0.0459490\pi\)
\(18\) 0 0
\(19\) 8.10051 + 14.0305i 0.0978096 + 0.169411i 0.910778 0.412897i \(-0.135483\pi\)
−0.812968 + 0.582308i \(0.802150\pi\)
\(20\) −63.5980 −0.711047
\(21\) 0 0
\(22\) −114.794 −1.11246
\(23\) −106.698 184.807i −0.967312 1.67543i −0.703271 0.710922i \(-0.748278\pi\)
−0.264041 0.964512i \(-0.585055\pi\)
\(24\) 0 0
\(25\) −63.8970 + 110.673i −0.511176 + 0.885382i
\(26\) 5.69848 + 9.87007i 0.0429833 + 0.0744492i
\(27\) 0 0
\(28\) 0 0
\(29\) 218.191 1.39714 0.698570 0.715542i \(-0.253820\pi\)
0.698570 + 0.715542i \(0.253820\pi\)
\(30\) 0 0
\(31\) −125.698 + 217.716i −0.728262 + 1.26139i 0.229356 + 0.973343i \(0.426338\pi\)
−0.957617 + 0.288044i \(0.906995\pi\)
\(32\) −16.0000 + 27.7128i −0.0883883 + 0.153093i
\(33\) 0 0
\(34\) −103.799 −0.523570
\(35\) 0 0
\(36\) 0 0
\(37\) −193.397 334.973i −0.859304 1.48836i −0.872593 0.488447i \(-0.837563\pi\)
0.0132889 0.999912i \(-0.495770\pi\)
\(38\) 16.2010 28.0610i 0.0691619 0.119792i
\(39\) 0 0
\(40\) 63.5980 + 110.155i 0.251393 + 0.435426i
\(41\) −328.503 −1.25130 −0.625652 0.780102i \(-0.715167\pi\)
−0.625652 + 0.780102i \(0.715167\pi\)
\(42\) 0 0
\(43\) −37.5879 −0.133305 −0.0666523 0.997776i \(-0.521232\pi\)
−0.0666523 + 0.997776i \(0.521232\pi\)
\(44\) 114.794 + 198.829i 0.393314 + 0.681241i
\(45\) 0 0
\(46\) −213.397 + 369.614i −0.683993 + 1.18471i
\(47\) 127.497 + 220.832i 0.395690 + 0.685355i 0.993189 0.116515i \(-0.0371722\pi\)
−0.597499 + 0.801869i \(0.703839\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 255.588 0.722912
\(51\) 0 0
\(52\) 11.3970 19.7401i 0.0303938 0.0526435i
\(53\) 105.794 183.240i 0.274187 0.474906i −0.695743 0.718291i \(-0.744925\pi\)
0.969930 + 0.243385i \(0.0782579\pi\)
\(54\) 0 0
\(55\) 912.583 2.23732
\(56\) 0 0
\(57\) 0 0
\(58\) −218.191 377.918i −0.493963 0.855569i
\(59\) 206.101 356.977i 0.454780 0.787701i −0.543896 0.839153i \(-0.683051\pi\)
0.998676 + 0.0514512i \(0.0163847\pi\)
\(60\) 0 0
\(61\) −418.347 724.598i −0.878095 1.52091i −0.853429 0.521210i \(-0.825481\pi\)
−0.0246666 0.999696i \(-0.507852\pi\)
\(62\) 502.794 1.02992
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) −45.3015 78.4645i −0.0864456 0.149728i
\(66\) 0 0
\(67\) 82.7939 143.403i 0.150969 0.261485i −0.780615 0.625012i \(-0.785094\pi\)
0.931584 + 0.363527i \(0.118427\pi\)
\(68\) 103.799 + 179.785i 0.185110 + 0.320620i
\(69\) 0 0
\(70\) 0 0
\(71\) 465.015 0.777284 0.388642 0.921389i \(-0.372944\pi\)
0.388642 + 0.921389i \(0.372944\pi\)
\(72\) 0 0
\(73\) 224.829 389.415i 0.360469 0.624351i −0.627569 0.778561i \(-0.715950\pi\)
0.988038 + 0.154210i \(0.0492833\pi\)
\(74\) −386.794 + 669.947i −0.607620 + 1.05243i
\(75\) 0 0
\(76\) −64.8040 −0.0978096
\(77\) 0 0
\(78\) 0 0
\(79\) 171.779 + 297.530i 0.244641 + 0.423730i 0.962031 0.272942i \(-0.0879966\pi\)
−0.717390 + 0.696672i \(0.754663\pi\)
\(80\) 127.196 220.310i 0.177762 0.307892i
\(81\) 0 0
\(82\) 328.503 + 568.983i 0.442403 + 0.766264i
\(83\) 1502.33 1.98677 0.993387 0.114812i \(-0.0366265\pi\)
0.993387 + 0.114812i \(0.0366265\pi\)
\(84\) 0 0
\(85\) 825.176 1.05298
\(86\) 37.5879 + 65.1041i 0.0471303 + 0.0816321i
\(87\) 0 0
\(88\) 229.588 397.658i 0.278115 0.481710i
\(89\) 170.543 + 295.389i 0.203118 + 0.351810i 0.949531 0.313672i \(-0.101559\pi\)
−0.746414 + 0.665482i \(0.768226\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 853.588 0.967312
\(93\) 0 0
\(94\) 254.995 441.664i 0.279795 0.484619i
\(95\) −128.794 + 223.078i −0.139095 + 0.240919i
\(96\) 0 0
\(97\) 865.437 0.905895 0.452947 0.891537i \(-0.350373\pi\)
0.452947 + 0.891537i \(0.350373\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −255.588 442.691i −0.255588 0.442691i
\(101\) 121.628 210.666i 0.119826 0.207545i −0.799873 0.600170i \(-0.795100\pi\)
0.919699 + 0.392625i \(0.128433\pi\)
\(102\) 0 0
\(103\) −476.673 825.622i −0.456000 0.789815i 0.542745 0.839898i \(-0.317385\pi\)
−0.998745 + 0.0500822i \(0.984052\pi\)
\(104\) −45.5879 −0.0429833
\(105\) 0 0
\(106\) −423.176 −0.387759
\(107\) −672.477 1164.76i −0.607578 1.05236i −0.991638 0.129048i \(-0.958808\pi\)
0.384061 0.923308i \(-0.374525\pi\)
\(108\) 0 0
\(109\) −867.176 + 1501.99i −0.762022 + 1.31986i 0.179785 + 0.983706i \(0.442460\pi\)
−0.941807 + 0.336155i \(0.890874\pi\)
\(110\) −912.583 1580.64i −0.791012 1.37007i
\(111\) 0 0
\(112\) 0 0
\(113\) −1441.18 −1.19977 −0.599887 0.800085i \(-0.704788\pi\)
−0.599887 + 0.800085i \(0.704788\pi\)
\(114\) 0 0
\(115\) 1696.45 2938.34i 1.37561 2.38262i
\(116\) −436.382 + 755.835i −0.349285 + 0.604979i
\(117\) 0 0
\(118\) −824.402 −0.643156
\(119\) 0 0
\(120\) 0 0
\(121\) −981.706 1700.36i −0.737570 1.27751i
\(122\) −836.693 + 1449.20i −0.620907 + 1.07544i
\(123\) 0 0
\(124\) −502.794 870.865i −0.364131 0.630693i
\(125\) −44.4222 −0.0317860
\(126\) 0 0
\(127\) 1184.70 0.827759 0.413880 0.910332i \(-0.364173\pi\)
0.413880 + 0.910332i \(0.364173\pi\)
\(128\) −64.0000 110.851i −0.0441942 0.0765466i
\(129\) 0 0
\(130\) −90.6030 + 156.929i −0.0611262 + 0.105874i
\(131\) −148.794 257.719i −0.0992381 0.171885i 0.812131 0.583475i \(-0.198307\pi\)
−0.911369 + 0.411589i \(0.864974\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −331.176 −0.213502
\(135\) 0 0
\(136\) 207.598 359.570i 0.130892 0.226712i
\(137\) 310.492 537.789i 0.193629 0.335375i −0.752821 0.658225i \(-0.771308\pi\)
0.946450 + 0.322850i \(0.104641\pi\)
\(138\) 0 0
\(139\) 898.754 0.548426 0.274213 0.961669i \(-0.411583\pi\)
0.274213 + 0.961669i \(0.411583\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −465.015 805.430i −0.274811 0.475987i
\(143\) −163.538 + 283.256i −0.0956344 + 0.165644i
\(144\) 0 0
\(145\) 1734.56 + 3004.35i 0.993432 + 1.72067i
\(146\) −899.316 −0.509780
\(147\) 0 0
\(148\) 1547.18 0.859304
\(149\) −1527.35 2645.45i −0.839769 1.45452i −0.890088 0.455789i \(-0.849357\pi\)
0.0503195 0.998733i \(-0.483976\pi\)
\(150\) 0 0
\(151\) 32.5727 56.4176i 0.0175545 0.0304053i −0.857115 0.515126i \(-0.827745\pi\)
0.874669 + 0.484720i \(0.161079\pi\)
\(152\) 64.8040 + 112.244i 0.0345809 + 0.0598959i
\(153\) 0 0
\(154\) 0 0
\(155\) −3997.08 −2.07131
\(156\) 0 0
\(157\) 771.110 1335.60i 0.391983 0.678934i −0.600728 0.799453i \(-0.705123\pi\)
0.992711 + 0.120519i \(0.0384559\pi\)
\(158\) 343.558 595.059i 0.172987 0.299623i
\(159\) 0 0
\(160\) −508.784 −0.251393
\(161\) 0 0
\(162\) 0 0
\(163\) 1257.37 + 2177.82i 0.604200 + 1.04650i 0.992177 + 0.124836i \(0.0398404\pi\)
−0.387978 + 0.921669i \(0.626826\pi\)
\(164\) 657.005 1137.97i 0.312826 0.541831i
\(165\) 0 0
\(166\) −1502.33 2602.11i −0.702431 1.21665i
\(167\) 528.643 0.244956 0.122478 0.992471i \(-0.460916\pi\)
0.122478 + 0.992471i \(0.460916\pi\)
\(168\) 0 0
\(169\) −2164.53 −0.985220
\(170\) −825.176 1429.25i −0.372283 0.644813i
\(171\) 0 0
\(172\) 75.1758 130.208i 0.0333261 0.0577226i
\(173\) −48.4220 83.8693i −0.0212801 0.0368582i 0.855189 0.518316i \(-0.173441\pi\)
−0.876469 + 0.481458i \(0.840108\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −918.352 −0.393314
\(177\) 0 0
\(178\) 341.085 590.777i 0.143626 0.248768i
\(179\) −267.271 + 462.927i −0.111602 + 0.193301i −0.916416 0.400226i \(-0.868932\pi\)
0.804814 + 0.593527i \(0.202265\pi\)
\(180\) 0 0
\(181\) −2087.00 −0.857049 −0.428524 0.903530i \(-0.640966\pi\)
−0.428524 + 0.903530i \(0.640966\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −853.588 1478.46i −0.341996 0.592355i
\(185\) 3074.91 5325.91i 1.22201 2.11659i
\(186\) 0 0
\(187\) −1489.44 2579.78i −0.582451 1.00884i
\(188\) −1019.98 −0.395690
\(189\) 0 0
\(190\) 515.176 0.196709
\(191\) 1693.84 + 2933.82i 0.641687 + 1.11143i 0.985056 + 0.172234i \(0.0550986\pi\)
−0.343369 + 0.939201i \(0.611568\pi\)
\(192\) 0 0
\(193\) 954.176 1652.68i 0.355871 0.616386i −0.631396 0.775461i \(-0.717518\pi\)
0.987267 + 0.159074i \(0.0508510\pi\)
\(194\) −865.437 1498.98i −0.320282 0.554745i
\(195\) 0 0
\(196\) 0 0
\(197\) 2061.88 0.745699 0.372850 0.927892i \(-0.378381\pi\)
0.372850 + 0.927892i \(0.378381\pi\)
\(198\) 0 0
\(199\) 1585.75 2746.60i 0.564878 0.978397i −0.432183 0.901786i \(-0.642257\pi\)
0.997061 0.0766115i \(-0.0244101\pi\)
\(200\) −511.176 + 885.382i −0.180728 + 0.313030i
\(201\) 0 0
\(202\) −486.512 −0.169460
\(203\) 0 0
\(204\) 0 0
\(205\) −2611.51 4523.27i −0.889736 1.54107i
\(206\) −953.346 + 1651.24i −0.322441 + 0.558484i
\(207\) 0 0
\(208\) 45.5879 + 78.9605i 0.0151969 + 0.0263218i
\(209\) 929.889 0.307760
\(210\) 0 0
\(211\) 1349.97 0.440454 0.220227 0.975449i \(-0.429320\pi\)
0.220227 + 0.975449i \(0.429320\pi\)
\(212\) 423.176 + 732.962i 0.137094 + 0.237453i
\(213\) 0 0
\(214\) −1344.95 + 2329.53i −0.429622 + 0.744128i
\(215\) −298.814 517.561i −0.0947858 0.164174i
\(216\) 0 0
\(217\) 0 0
\(218\) 3468.70 1.07766
\(219\) 0 0
\(220\) −1825.17 + 3161.28i −0.559330 + 0.968788i
\(221\) −147.874 + 256.126i −0.0450095 + 0.0779587i
\(222\) 0 0
\(223\) 1361.85 0.408951 0.204476 0.978872i \(-0.434451\pi\)
0.204476 + 0.978872i \(0.434451\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 1441.18 + 2496.19i 0.424184 + 0.734708i
\(227\) −930.905 + 1612.37i −0.272186 + 0.471441i −0.969421 0.245402i \(-0.921080\pi\)
0.697235 + 0.716843i \(0.254413\pi\)
\(228\) 0 0
\(229\) −2679.39 4640.84i −0.773184 1.33919i −0.935809 0.352506i \(-0.885329\pi\)
0.162625 0.986688i \(-0.448004\pi\)
\(230\) −6785.81 −1.94540
\(231\) 0 0
\(232\) 1745.53 0.493963
\(233\) 2720.56 + 4712.15i 0.764935 + 1.32491i 0.940281 + 0.340400i \(0.110562\pi\)
−0.175345 + 0.984507i \(0.556104\pi\)
\(234\) 0 0
\(235\) −2027.15 + 3511.12i −0.562708 + 0.974639i
\(236\) 824.402 + 1427.91i 0.227390 + 0.393851i
\(237\) 0 0
\(238\) 0 0
\(239\) 1157.28 0.313213 0.156607 0.987661i \(-0.449945\pi\)
0.156607 + 0.987661i \(0.449945\pi\)
\(240\) 0 0
\(241\) −1984.69 + 3437.58i −0.530477 + 0.918814i 0.468890 + 0.883256i \(0.344654\pi\)
−0.999368 + 0.0355573i \(0.988679\pi\)
\(242\) −1963.41 + 3400.73i −0.521541 + 0.903335i
\(243\) 0 0
\(244\) 3346.77 0.878095
\(245\) 0 0
\(246\) 0 0
\(247\) −46.1606 79.9525i −0.0118912 0.0205962i
\(248\) −1005.59 + 1741.73i −0.257479 + 0.445967i
\(249\) 0 0
\(250\) 44.4222 + 76.9415i 0.0112380 + 0.0194648i
\(251\) 5978.75 1.50349 0.751744 0.659455i \(-0.229213\pi\)
0.751744 + 0.659455i \(0.229213\pi\)
\(252\) 0 0
\(253\) −12248.3 −3.04366
\(254\) −1184.70 2051.97i −0.292657 0.506897i
\(255\) 0 0
\(256\) −128.000 + 221.703i −0.0312500 + 0.0541266i
\(257\) −2325.07 4027.15i −0.564335 0.977458i −0.997111 0.0759560i \(-0.975799\pi\)
0.432776 0.901502i \(-0.357534\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 362.412 0.0864456
\(261\) 0 0
\(262\) −297.588 + 515.437i −0.0701719 + 0.121541i
\(263\) 1847.68 3200.28i 0.433205 0.750334i −0.563942 0.825815i \(-0.690716\pi\)
0.997147 + 0.0754807i \(0.0240491\pi\)
\(264\) 0 0
\(265\) 3364.14 0.779840
\(266\) 0 0
\(267\) 0 0
\(268\) 331.176 + 573.613i 0.0754843 + 0.130743i
\(269\) 3578.84 6198.74i 0.811175 1.40500i −0.100868 0.994900i \(-0.532162\pi\)
0.912042 0.410096i \(-0.134505\pi\)
\(270\) 0 0
\(271\) 2019.19 + 3497.33i 0.452608 + 0.783940i 0.998547 0.0538847i \(-0.0171604\pi\)
−0.545939 + 0.837825i \(0.683827\pi\)
\(272\) −830.392 −0.185110
\(273\) 0 0
\(274\) −1241.97 −0.273833
\(275\) 3667.49 + 6352.28i 0.804211 + 1.39293i
\(276\) 0 0
\(277\) 1377.41 2385.75i 0.298775 0.517493i −0.677081 0.735909i \(-0.736755\pi\)
0.975856 + 0.218415i \(0.0700887\pi\)
\(278\) −898.754 1556.69i −0.193898 0.335841i
\(279\) 0 0
\(280\) 0 0
\(281\) 772.742 0.164050 0.0820248 0.996630i \(-0.473861\pi\)
0.0820248 + 0.996630i \(0.473861\pi\)
\(282\) 0 0
\(283\) −3372.74 + 5841.76i −0.708441 + 1.22706i 0.256995 + 0.966413i \(0.417268\pi\)
−0.965435 + 0.260643i \(0.916066\pi\)
\(284\) −930.030 + 1610.86i −0.194321 + 0.336574i
\(285\) 0 0
\(286\) 654.152 0.135248
\(287\) 0 0
\(288\) 0 0
\(289\) 1109.72 + 1922.09i 0.225874 + 0.391226i
\(290\) 3469.13 6008.70i 0.702462 1.21670i
\(291\) 0 0
\(292\) 899.316 + 1557.66i 0.180235 + 0.312175i
\(293\) 1922.69 0.383362 0.191681 0.981457i \(-0.438606\pi\)
0.191681 + 0.981457i \(0.438606\pi\)
\(294\) 0 0
\(295\) 6553.79 1.29348
\(296\) −1547.18 2679.79i −0.303810 0.526214i
\(297\) 0 0
\(298\) −3054.70 + 5290.90i −0.593806 + 1.02850i
\(299\) 608.020 + 1053.12i 0.117601 + 0.203691i
\(300\) 0 0
\(301\) 0 0
\(302\) −130.291 −0.0248258
\(303\) 0 0
\(304\) 129.608 224.488i 0.0244524 0.0423528i
\(305\) 6651.50 11520.7i 1.24873 2.16287i
\(306\) 0 0
\(307\) −2016.68 −0.374913 −0.187456 0.982273i \(-0.560024\pi\)
−0.187456 + 0.982273i \(0.560024\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 3997.08 + 6923.15i 0.732320 + 1.26842i
\(311\) −3574.99 + 6192.07i −0.651831 + 1.12900i 0.330848 + 0.943684i \(0.392665\pi\)
−0.982678 + 0.185320i \(0.940668\pi\)
\(312\) 0 0
\(313\) 4298.25 + 7444.78i 0.776202 + 1.34442i 0.934116 + 0.356969i \(0.116190\pi\)
−0.157914 + 0.987453i \(0.550477\pi\)
\(314\) −3084.44 −0.554347
\(315\) 0 0
\(316\) −1374.23 −0.244641
\(317\) −1426.62 2470.98i −0.252766 0.437804i 0.711520 0.702666i \(-0.248007\pi\)
−0.964286 + 0.264862i \(0.914674\pi\)
\(318\) 0 0
\(319\) 6261.75 10845.7i 1.09903 1.90358i
\(320\) 508.784 + 881.239i 0.0888809 + 0.153946i
\(321\) 0 0
\(322\) 0 0
\(323\) 840.824 0.144844
\(324\) 0 0
\(325\) 364.116 630.667i 0.0621462 0.107640i
\(326\) 2514.73 4355.65i 0.427234 0.739991i
\(327\) 0 0
\(328\) −2628.02 −0.442403
\(329\) 0 0
\(330\) 0 0
\(331\) −809.558 1402.19i −0.134433 0.232845i 0.790948 0.611884i \(-0.209588\pi\)
−0.925381 + 0.379039i \(0.876255\pi\)
\(332\) −3004.66 + 5204.23i −0.496694 + 0.860299i
\(333\) 0 0
\(334\) −528.643 915.637i −0.0866050 0.150004i
\(335\) 2632.76 0.429383
\(336\) 0 0
\(337\) −3278.67 −0.529972 −0.264986 0.964252i \(-0.585367\pi\)
−0.264986 + 0.964252i \(0.585367\pi\)
\(338\) 2164.53 + 3749.07i 0.348328 + 0.603321i
\(339\) 0 0
\(340\) −1650.35 + 2858.49i −0.263244 + 0.455952i
\(341\) 7214.71 + 12496.2i 1.14574 + 1.98449i
\(342\) 0 0
\(343\) 0 0
\(344\) −300.703 −0.0471303
\(345\) 0 0
\(346\) −96.8439 + 167.739i −0.0150473 + 0.0260627i
\(347\) −1425.15 + 2468.43i −0.220479 + 0.381880i −0.954953 0.296756i \(-0.904095\pi\)
0.734475 + 0.678636i \(0.237429\pi\)
\(348\) 0 0
\(349\) 4725.32 0.724758 0.362379 0.932031i \(-0.381965\pi\)
0.362379 + 0.932031i \(0.381965\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 918.352 + 1590.63i 0.139058 + 0.240855i
\(353\) −3363.72 + 5826.13i −0.507175 + 0.878452i 0.492791 + 0.870148i \(0.335977\pi\)
−0.999966 + 0.00830453i \(0.997357\pi\)
\(354\) 0 0
\(355\) 3696.75 + 6402.96i 0.552685 + 0.957279i
\(356\) −1364.34 −0.203118
\(357\) 0 0
\(358\) 1069.08 0.157829
\(359\) −3665.94 6349.60i −0.538945 0.933479i −0.998961 0.0455691i \(-0.985490\pi\)
0.460017 0.887910i \(-0.347843\pi\)
\(360\) 0 0
\(361\) 3298.26 5712.76i 0.480867 0.832885i
\(362\) 2087.00 + 3614.80i 0.303012 + 0.524833i
\(363\) 0 0
\(364\) 0 0
\(365\) 7149.34 1.02524
\(366\) 0 0
\(367\) 1387.22 2402.73i 0.197308 0.341748i −0.750347 0.661045i \(-0.770113\pi\)
0.947655 + 0.319297i \(0.103447\pi\)
\(368\) −1707.18 + 2956.92i −0.241828 + 0.418858i
\(369\) 0 0
\(370\) −12299.7 −1.72819
\(371\) 0 0
\(372\) 0 0
\(373\) −1263.67 2188.75i −0.175417 0.303831i 0.764889 0.644163i \(-0.222794\pi\)
−0.940305 + 0.340332i \(0.889461\pi\)
\(374\) −2978.87 + 5159.56i −0.411855 + 0.713354i
\(375\) 0 0
\(376\) 1019.98 + 1766.66i 0.139897 + 0.242309i
\(377\) −1243.36 −0.169857
\(378\) 0 0
\(379\) 3116.40 0.422371 0.211186 0.977446i \(-0.432268\pi\)
0.211186 + 0.977446i \(0.432268\pi\)
\(380\) −515.176 892.311i −0.0695473 0.120459i
\(381\) 0 0
\(382\) 3387.69 5867.65i 0.453741 0.785903i
\(383\) −759.035 1314.69i −0.101266 0.175398i 0.810940 0.585129i \(-0.198956\pi\)
−0.912207 + 0.409731i \(0.865623\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −3816.70 −0.503277
\(387\) 0 0
\(388\) −1730.87 + 2997.96i −0.226474 + 0.392264i
\(389\) −1623.39 + 2811.79i −0.211591 + 0.366487i −0.952213 0.305436i \(-0.901198\pi\)
0.740622 + 0.671922i \(0.234531\pi\)
\(390\) 0 0
\(391\) −11075.2 −1.43247
\(392\) 0 0
\(393\) 0 0
\(394\) −2061.88 3571.28i −0.263645 0.456646i
\(395\) −2731.20 + 4730.57i −0.347902 + 0.602584i
\(396\) 0 0
\(397\) −915.312 1585.37i −0.115713 0.200421i 0.802351 0.596852i \(-0.203582\pi\)
−0.918065 + 0.396431i \(0.870249\pi\)
\(398\) −6342.99 −0.798858
\(399\) 0 0
\(400\) 2044.70 0.255588
\(401\) −1692.90 2932.20i −0.210822 0.365154i 0.741150 0.671339i \(-0.234281\pi\)
−0.951972 + 0.306185i \(0.900947\pi\)
\(402\) 0 0
\(403\) 716.291 1240.65i 0.0885384 0.153353i
\(404\) 486.512 + 842.664i 0.0599131 + 0.103772i
\(405\) 0 0
\(406\) 0 0
\(407\) −22200.8 −2.70382
\(408\) 0 0
\(409\) −4626.59 + 8013.48i −0.559340 + 0.968805i 0.438212 + 0.898872i \(0.355612\pi\)
−0.997552 + 0.0699333i \(0.977721\pi\)
\(410\) −5223.02 + 9046.54i −0.629138 + 1.08970i
\(411\) 0 0
\(412\) 3813.39 0.456000
\(413\) 0 0
\(414\) 0 0
\(415\) 11943.2 + 20686.2i 1.41269 + 2.44685i
\(416\) 91.1758 157.921i 0.0107458 0.0186123i
\(417\) 0 0
\(418\) −929.889 1610.61i −0.108809 0.188464i
\(419\) −3547.52 −0.413622 −0.206811 0.978381i \(-0.566308\pi\)
−0.206811 + 0.978381i \(0.566308\pi\)
\(420\) 0 0
\(421\) 7848.87 0.908624 0.454312 0.890843i \(-0.349885\pi\)
0.454312 + 0.890843i \(0.349885\pi\)
\(422\) −1349.97 2338.22i −0.155724 0.269722i
\(423\) 0 0
\(424\) 846.352 1465.92i 0.0969398 0.167905i
\(425\) 3316.22 + 5743.86i 0.378495 + 0.655572i
\(426\) 0 0
\(427\) 0 0
\(428\) 5379.82 0.607578
\(429\) 0 0
\(430\) −597.628 + 1035.12i −0.0670237 + 0.116088i
\(431\) −2223.66 + 3851.50i −0.248515 + 0.430441i −0.963114 0.269094i \(-0.913276\pi\)
0.714599 + 0.699534i \(0.246609\pi\)
\(432\) 0 0
\(433\) −6994.82 −0.776327 −0.388164 0.921590i \(-0.626890\pi\)
−0.388164 + 0.921590i \(0.626890\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −3468.70 6007.97i −0.381011 0.659930i
\(437\) 1728.62 2994.06i 0.189225 0.327747i
\(438\) 0 0
\(439\) −318.091 550.950i −0.0345823 0.0598984i 0.848216 0.529650i \(-0.177677\pi\)
−0.882799 + 0.469752i \(0.844343\pi\)
\(440\) 7300.66 0.791012
\(441\) 0 0
\(442\) 591.497 0.0636530
\(443\) −2237.12 3874.80i −0.239929 0.415570i 0.720764 0.693180i \(-0.243791\pi\)
−0.960694 + 0.277610i \(0.910458\pi\)
\(444\) 0 0
\(445\) −2711.54 + 4696.53i −0.288853 + 0.500308i
\(446\) −1361.85 2358.79i −0.144586 0.250430i
\(447\) 0 0
\(448\) 0 0
\(449\) 2389.42 0.251144 0.125572 0.992085i \(-0.459923\pi\)
0.125572 + 0.992085i \(0.459923\pi\)
\(450\) 0 0
\(451\) −9427.52 + 16329.0i −0.984312 + 1.70488i
\(452\) 2882.35 4992.38i 0.299943 0.519517i
\(453\) 0 0
\(454\) 3723.62 0.384930
\(455\) 0 0
\(456\) 0 0
\(457\) 2219.17 + 3843.71i 0.227152 + 0.393438i 0.956963 0.290210i \(-0.0937253\pi\)
−0.729811 + 0.683649i \(0.760392\pi\)
\(458\) −5358.78 + 9281.68i −0.546724 + 0.946953i
\(459\) 0 0
\(460\) 6785.81 + 11753.4i 0.687804 + 1.19131i
\(461\) 14079.8 1.42248 0.711240 0.702949i \(-0.248134\pi\)
0.711240 + 0.702949i \(0.248134\pi\)
\(462\) 0 0
\(463\) 4687.50 0.470511 0.235255 0.971934i \(-0.424407\pi\)
0.235255 + 0.971934i \(0.424407\pi\)
\(464\) −1745.53 3023.34i −0.174642 0.302489i
\(465\) 0 0
\(466\) 5441.12 9424.30i 0.540891 0.936851i
\(467\) 4223.63 + 7315.54i 0.418514 + 0.724888i 0.995790 0.0916611i \(-0.0292176\pi\)
−0.577276 + 0.816549i \(0.695884\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 8108.58 0.795789
\(471\) 0 0
\(472\) 1648.80 2855.81i 0.160789 0.278495i
\(473\) −1078.72 + 1868.39i −0.104861 + 0.181625i
\(474\) 0 0
\(475\) −2070.39 −0.199992
\(476\) 0 0
\(477\) 0 0
\(478\) −1157.28 2004.46i −0.110738 0.191803i
\(479\) −2184.70 + 3784.02i −0.208396 + 0.360952i −0.951209 0.308546i \(-0.900158\pi\)
0.742814 + 0.669498i \(0.233491\pi\)
\(480\) 0 0
\(481\) 1102.07 + 1908.84i 0.104470 + 0.180947i
\(482\) 7938.75 0.750208
\(483\) 0 0
\(484\) 7853.65 0.737570
\(485\) 6880.00 + 11916.5i 0.644134 + 1.11567i
\(486\) 0 0
\(487\) 7238.86 12538.1i 0.673561 1.16664i −0.303326 0.952887i \(-0.598097\pi\)
0.976887 0.213755i \(-0.0685695\pi\)
\(488\) −3346.77 5796.78i −0.310454 0.537721i
\(489\) 0 0
\(490\) 0 0
\(491\) −9306.12 −0.855355 −0.427677 0.903931i \(-0.640668\pi\)
−0.427677 + 0.903931i \(0.640668\pi\)
\(492\) 0 0
\(493\) 5662.00 9806.87i 0.517249 0.895901i
\(494\) −92.3212 + 159.905i −0.00840836 + 0.0145637i
\(495\) 0 0
\(496\) 4022.35 0.364131
\(497\) 0 0
\(498\) 0 0
\(499\) 6118.77 + 10598.0i 0.548926 + 0.950767i 0.998349 + 0.0574479i \(0.0182963\pi\)
−0.449423 + 0.893319i \(0.648370\pi\)
\(500\) 88.8444 153.883i 0.00794649 0.0137637i
\(501\) 0 0
\(502\) −5978.75 10355.5i −0.531563 0.920695i
\(503\) −5524.30 −0.489694 −0.244847 0.969562i \(-0.578738\pi\)
−0.244847 + 0.969562i \(0.578738\pi\)
\(504\) 0 0
\(505\) 3867.65 0.340808
\(506\) 12248.3 + 21214.7i 1.07610 + 1.86385i
\(507\) 0 0
\(508\) −2369.41 + 4103.93i −0.206940 + 0.358430i
\(509\) −5039.81 8729.20i −0.438871 0.760148i 0.558731 0.829349i \(-0.311288\pi\)
−0.997603 + 0.0692012i \(0.977955\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 512.000 0.0441942
\(513\) 0 0
\(514\) −4650.15 + 8054.30i −0.399045 + 0.691167i
\(515\) 7578.86 13127.0i 0.648475 1.12319i
\(516\) 0 0
\(517\) 14635.9 1.24504
\(518\) 0 0
\(519\) 0 0
\(520\) −362.412 627.716i −0.0305631 0.0529369i
\(521\) 2853.31 4942.07i 0.239934 0.415578i −0.720761 0.693184i \(-0.756208\pi\)
0.960695 + 0.277606i \(0.0895409\pi\)
\(522\) 0 0
\(523\) 5328.63 + 9229.46i 0.445516 + 0.771656i 0.998088 0.0618088i \(-0.0196869\pi\)
−0.552572 + 0.833465i \(0.686354\pi\)
\(524\) 1190.35 0.0992381
\(525\) 0 0
\(526\) −7390.73 −0.612645
\(527\) 6523.69 + 11299.4i 0.539234 + 0.933981i
\(528\) 0 0
\(529\) −16685.6 + 28900.4i −1.37138 + 2.37531i
\(530\) −3364.14 5826.86i −0.275715 0.477552i
\(531\) 0 0
\(532\) 0 0
\(533\) 1871.97 0.152127
\(534\) 0 0
\(535\) 10692.0 18519.2i 0.864033 1.49655i
\(536\) 662.352 1147.23i 0.0533754 0.0924489i
\(537\) 0 0
\(538\) −14315.4 −1.14717
\(539\) 0 0
\(540\) 0 0
\(541\) 2005.24 + 3473.18i 0.159357 + 0.276014i 0.934637 0.355603i \(-0.115725\pi\)
−0.775280 + 0.631618i \(0.782391\pi\)
\(542\) 4038.37 6994.66i 0.320042 0.554329i
\(543\) 0 0
\(544\) 830.392 + 1438.28i 0.0654462 + 0.113356i
\(545\) −27575.3 −2.16733
\(546\) 0 0
\(547\) −17619.8 −1.37728 −0.688638 0.725105i \(-0.741791\pi\)
−0.688638 + 0.725105i \(0.741791\pi\)
\(548\) 1241.97 + 2151.15i 0.0968144 + 0.167688i
\(549\) 0 0
\(550\) 7334.98 12704.6i 0.568663 0.984954i
\(551\) 1767.46 + 3061.32i 0.136654 + 0.236691i
\(552\) 0 0
\(553\) 0 0
\(554\) −5509.65 −0.422532
\(555\) 0 0
\(556\) −1797.51 + 3113.37i −0.137107 + 0.237476i
\(557\) −5168.85 + 8952.71i −0.393198 + 0.681038i −0.992869 0.119208i \(-0.961965\pi\)
0.599672 + 0.800246i \(0.295298\pi\)
\(558\) 0 0
\(559\) 214.194 0.0162065
\(560\) 0 0
\(561\) 0 0
\(562\) −772.742 1338.43i −0.0580003 0.100459i
\(563\) −12011.8 + 20805.1i −0.899180 + 1.55742i −0.0706347 + 0.997502i \(0.522502\pi\)
−0.828545 + 0.559923i \(0.810831\pi\)
\(564\) 0 0
\(565\) −11457.0 19844.1i −0.853095 1.47760i
\(566\) 13491.0 1.00189
\(567\) 0 0
\(568\) 3720.12 0.274811
\(569\) −6589.59 11413.5i −0.485501 0.840912i 0.514361 0.857574i \(-0.328029\pi\)
−0.999861 + 0.0166623i \(0.994696\pi\)
\(570\) 0 0
\(571\) −3888.13 + 6734.44i −0.284962 + 0.493568i −0.972600 0.232485i \(-0.925314\pi\)
0.687638 + 0.726054i \(0.258648\pi\)
\(572\) −654.152 1133.02i −0.0478172 0.0828219i
\(573\) 0 0
\(574\) 0 0
\(575\) 27270.8 1.97787
\(576\) 0 0
\(577\) −10083.5 + 17465.2i −0.727525 + 1.26011i 0.230401 + 0.973096i \(0.425996\pi\)
−0.957926 + 0.287015i \(0.907337\pi\)
\(578\) 2219.44 3844.19i 0.159717 0.276639i
\(579\) 0 0
\(580\) −13876.5 −0.993432
\(581\) 0 0
\(582\) 0 0
\(583\) −6072.25 10517.4i −0.431367 0.747150i
\(584\) 1798.63 3115.32i 0.127445 0.220741i
\(585\) 0 0
\(586\) −1922.69 3330.20i −0.135539 0.234760i
\(587\) 8365.08 0.588184 0.294092 0.955777i \(-0.404983\pi\)
0.294092 + 0.955777i \(0.404983\pi\)
\(588\) 0 0
\(589\) −4072.88 −0.284924
\(590\) −6553.79 11351.5i −0.457314 0.792091i
\(591\) 0 0
\(592\) −3094.35 + 5359.57i −0.214826 + 0.372090i
\(593\) −13810.9 23921.2i −0.956403 1.65654i −0.731124 0.682244i \(-0.761004\pi\)
−0.225279 0.974294i \(-0.572329\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 12218.8 0.839769
\(597\) 0 0
\(598\) 1216.04 2106.24i 0.0831564 0.144031i
\(599\) 269.159 466.197i 0.0183598 0.0318002i −0.856700 0.515816i \(-0.827489\pi\)
0.875059 + 0.484016i \(0.160822\pi\)
\(600\) 0 0
\(601\) 6958.64 0.472294 0.236147 0.971717i \(-0.424115\pi\)
0.236147 + 0.971717i \(0.424115\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 130.291 + 225.670i 0.00877725 + 0.0152027i
\(605\) 15608.6 27034.9i 1.04889 1.81674i
\(606\) 0 0
\(607\) 8648.80 + 14980.2i 0.578326 + 1.00169i 0.995671 + 0.0929425i \(0.0296273\pi\)
−0.417345 + 0.908748i \(0.637039\pi\)
\(608\) −518.432 −0.0345809
\(609\) 0 0
\(610\) −26606.0 −1.76598
\(611\) −726.542 1258.41i −0.0481060 0.0833220i
\(612\) 0 0
\(613\) 419.579 726.732i 0.0276454 0.0478832i −0.851872 0.523751i \(-0.824532\pi\)
0.879517 + 0.475867i \(0.157866\pi\)
\(614\) 2016.68 + 3493.00i 0.132552 + 0.229586i
\(615\) 0 0
\(616\) 0 0
\(617\) 16040.0 1.04659 0.523295 0.852152i \(-0.324703\pi\)
0.523295 + 0.852152i \(0.324703\pi\)
\(618\) 0 0
\(619\) 2714.64 4701.90i 0.176269 0.305307i −0.764331 0.644825i \(-0.776930\pi\)
0.940600 + 0.339517i \(0.110264\pi\)
\(620\) 7994.17 13846.3i 0.517828 0.896905i
\(621\) 0 0
\(622\) 14300.0 0.921828
\(623\) 0 0
\(624\) 0 0
\(625\) 7633.98 + 13222.4i 0.488574 + 0.846236i
\(626\) 8596.49 14889.6i 0.548858 0.950649i
\(627\) 0 0
\(628\) 3084.44 + 5342.41i 0.195991 + 0.339467i
\(629\) −20074.4 −1.27253
\(630\) 0 0
\(631\) −1807.86 −0.114057 −0.0570284 0.998373i \(-0.518163\pi\)
−0.0570284 + 0.998373i \(0.518163\pi\)
\(632\) 1374.23 + 2380.24i 0.0864936 + 0.149811i
\(633\) 0 0
\(634\) −2853.24 + 4941.95i −0.178733 + 0.309574i
\(635\) 9418.09 + 16312.6i 0.588576 + 1.01944i
\(636\) 0 0
\(637\) 0 0
\(638\) −25047.0 −1.55426
\(639\) 0 0
\(640\) 1017.57 1762.48i 0.0628483 0.108856i
\(641\) −2952.28 + 5113.50i −0.181916 + 0.315087i −0.942533 0.334113i \(-0.891563\pi\)
0.760617 + 0.649201i \(0.224897\pi\)
\(642\) 0 0
\(643\) 8092.42 0.496320 0.248160 0.968719i \(-0.420174\pi\)
0.248160 + 0.968719i \(0.420174\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −840.824 1456.35i −0.0512102 0.0886987i
\(647\) 10096.3 17487.4i 0.613490 1.06260i −0.377157 0.926149i \(-0.623098\pi\)
0.990647 0.136447i \(-0.0435683\pi\)
\(648\) 0 0
\(649\) −11829.5 20489.4i −0.715486 1.23926i
\(650\) −1456.46 −0.0878880
\(651\) 0 0
\(652\) −10058.9 −0.604200
\(653\) −10590.4 18343.2i −0.634664 1.09927i −0.986586 0.163240i \(-0.947805\pi\)
0.351923 0.936029i \(-0.385528\pi\)
\(654\) 0 0
\(655\) 2365.75 4097.60i 0.141126 0.244437i
\(656\) 2628.02 + 4551.86i 0.156413 + 0.270915i
\(657\) 0 0
\(658\) 0 0
\(659\) −28411.3 −1.67944 −0.839718 0.543023i \(-0.817280\pi\)
−0.839718 + 0.543023i \(0.817280\pi\)
\(660\) 0 0
\(661\) −8352.47 + 14466.9i −0.491488 + 0.851282i −0.999952 0.00980149i \(-0.996880\pi\)
0.508464 + 0.861083i \(0.330213\pi\)
\(662\) −1619.12 + 2804.39i −0.0950585 + 0.164646i
\(663\) 0 0
\(664\) 12018.7 0.702431
\(665\) 0 0
\(666\) 0 0
\(667\) −23280.6 40323.3i −1.35147 2.34081i
\(668\) −1057.29 + 1831.27i −0.0612390 + 0.106069i
\(669\) 0 0
\(670\) −2632.76 4560.08i −0.151810 0.262942i
\(671\) −48023.7 −2.76294
\(672\) 0 0
\(673\) −9047.09 −0.518187 −0.259093 0.965852i \(-0.583424\pi\)
−0.259093 + 0.965852i \(0.583424\pi\)
\(674\) 3278.67 + 5678.83i 0.187374 + 0.324540i
\(675\) 0 0
\(676\) 4329.05 7498.14i 0.246305 0.426613i
\(677\) −3922.13 6793.32i −0.222658 0.385655i 0.732956 0.680276i \(-0.238140\pi\)
−0.955614 + 0.294621i \(0.904807\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 6601.41 0.372283
\(681\) 0 0
\(682\) 14429.4 24992.5i 0.810163 1.40324i
\(683\) 12883.0 22314.1i 0.721751 1.25011i −0.238547 0.971131i \(-0.576671\pi\)
0.960298 0.278978i \(-0.0899956\pi\)
\(684\) 0 0
\(685\) 9873.35 0.550717
\(686\) 0 0
\(687\) 0 0
\(688\) 300.703 + 520.833i 0.0166631 + 0.0288613i
\(689\) −602.865 + 1044.19i −0.0333343 + 0.0577367i
\(690\) 0 0
\(691\) −12337.1 21368.4i −0.679195 1.17640i −0.975224 0.221221i \(-0.928996\pi\)
0.296029 0.955179i \(-0.404338\pi\)
\(692\) 387.376 0.0212801
\(693\) 0 0
\(694\) 5700.60 0.311804
\(695\) 7144.86 + 12375.3i 0.389957 + 0.675425i
\(696\) 0 0
\(697\) −8524.56 + 14765.0i −0.463258 + 0.802386i
\(698\) −4725.32 8184.49i −0.256241 0.443822i
\(699\) 0 0
\(700\) 0 0
\(701\) −29377.9 −1.58286 −0.791431 0.611258i \(-0.790664\pi\)
−0.791431 + 0.611258i \(0.790664\pi\)
\(702\) 0 0
\(703\) 3133.23 5426.91i 0.168097 0.291152i
\(704\) 1836.70 3181.26i 0.0983286 0.170310i
\(705\) 0 0
\(706\) 13454.9 0.717253
\(707\) 0 0
\(708\) 0 0
\(709\) −15297.1 26495.4i −0.810291 1.40347i −0.912660 0.408719i \(-0.865976\pi\)
0.102369 0.994746i \(-0.467358\pi\)
\(710\) 7393.51 12805.9i 0.390808 0.676898i
\(711\) 0 0
\(712\) 1364.34 + 2363.11i 0.0718130 + 0.124384i
\(713\) 53647.4 2.81782
\(714\) 0 0
\(715\) −5200.34 −0.272002
\(716\) −1069.08 1851.71i −0.0558011 0.0966503i
\(717\) 0 0
\(718\) −7331.89 + 12699.2i −0.381091 + 0.660070i
\(719\) 973.469 + 1686.10i 0.0504927 + 0.0874559i 0.890167 0.455634i \(-0.150588\pi\)
−0.839674 + 0.543090i \(0.817254\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −13193.1 −0.680048
\(723\) 0 0
\(724\) 4174.01 7229.60i 0.214262 0.371113i
\(725\) −13941.7 + 24147.8i −0.714184 + 1.23700i
\(726\) 0 0
\(727\) −15750.6 −0.803518 −0.401759 0.915745i \(-0.631601\pi\)
−0.401759 + 0.915745i \(0.631601\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −7149.34 12383.0i −0.362478 0.627830i
\(731\) −975.396 + 1689.44i −0.0493520 + 0.0854802i
\(732\) 0 0
\(733\) 7174.78 + 12427.1i 0.361537 + 0.626200i 0.988214 0.153079i \(-0.0489189\pi\)
−0.626677 + 0.779279i \(0.715586\pi\)
\(734\) −5548.86 −0.279036
\(735\) 0 0
\(736\) 6828.70 0.341996
\(737\) −4752.12 8230.92i −0.237512 0.411384i
\(738\) 0 0
\(739\) 8879.03 15378.9i 0.441976 0.765525i −0.555860 0.831276i \(-0.687611\pi\)
0.997836 + 0.0657506i \(0.0209442\pi\)
\(740\) 12299.7 + 21303.6i 0.611006 + 1.05829i
\(741\) 0 0
\(742\) 0 0
\(743\) 29187.6 1.44117 0.720586 0.693366i \(-0.243873\pi\)
0.720586 + 0.693366i \(0.243873\pi\)
\(744\) 0 0
\(745\) 24284.1 42061.3i 1.19423 2.06847i
\(746\) −2527.35 + 4377.49i −0.124038 + 0.214841i
\(747\) 0 0
\(748\) 11915.5 0.582451
\(749\) 0 0
\(750\) 0 0
\(751\) −6890.97 11935.5i −0.334827 0.579938i 0.648624 0.761109i \(-0.275345\pi\)
−0.983452 + 0.181171i \(0.942011\pi\)
\(752\) 2039.96 3533.31i 0.0989224 0.171339i
\(753\) 0 0
\(754\) 1243.36 + 2153.56i 0.0600536 + 0.104016i
\(755\) 1035.78 0.0499283
\(756\) 0 0
\(757\) 36952.7 1.77420 0.887099 0.461579i \(-0.152717\pi\)
0.887099 + 0.461579i \(0.152717\pi\)
\(758\) −3116.40 5397.76i −0.149331 0.258649i
\(759\) 0 0
\(760\) −1030.35 + 1784.62i −0.0491773 + 0.0851776i
\(761\) −14408.2 24955.8i −0.686332 1.18876i −0.973016 0.230737i \(-0.925886\pi\)
0.286684 0.958025i \(-0.407447\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −13550.8 −0.641687
\(765\) 0 0
\(766\) −1518.07 + 2629.38i −0.0716059 + 0.124025i
\(767\) −1174.46 + 2034.23i −0.0552898 + 0.0957648i
\(768\) 0 0
\(769\) −25285.2 −1.18571 −0.592854 0.805310i \(-0.701999\pi\)
−0.592854 + 0.805310i \(0.701999\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 3816.70 + 6610.72i 0.177935 + 0.308193i
\(773\) 9209.10 15950.6i 0.428497 0.742179i −0.568243 0.822861i \(-0.692376\pi\)
0.996740 + 0.0806820i \(0.0257098\pi\)
\(774\) 0 0
\(775\) −16063.5 27822.8i −0.744540 1.28958i
\(776\) 6923.49 0.320282
\(777\) 0 0
\(778\) 6493.55 0.299235
\(779\) −2661.04 4609.05i −0.122390 0.211985i
\(780\) 0 0
\(781\) 13345.2 23114.6i 0.611434 1.05903i
\(782\) 11075.2 + 19182.8i 0.506455 + 0.877207i
\(783\) 0 0
\(784\) 0 0
\(785\) 24520.5 1.11487
\(786\) 0 0
\(787\) −5537.90 + 9591.92i −0.250832 + 0.434454i −0.963755 0.266788i \(-0.914038\pi\)
0.712923 + 0.701242i \(0.247371\pi\)
\(788\) −4123.76 + 7142.56i −0.186425 + 0.322897i
\(789\) 0 0
\(790\) 10924.8 0.492008
\(791\) 0